Introduction – What is calculus?
Chapter 2 – Limits and derivatives
2.1 The tangent and velocity problems 2.2 The limit of a function 2.3 Calculating limits using the limit laws 2.4 The precise definition of a limit 2.5 Continuity 2.6 Limits at infinity; horizontal asymptotes 2.7 Derivatives and rates of change 2.8 The derivative as a function
Chapter 3 – Differentiation Rules
3.1 Derivatives of polynomials and exponential functions; see also 1.5 3.2 The Product and Quotient Rules 3.3 Derivatives of trigonometric functions 3.4 The Chain Rule 3.5 Implicit differentiation 3.6 Derivatives of logarithmic functions; see also 1.6 3.7 Rates of change in the natural and social sciences 3.8 Exponential growth and decay 3.9 Related rates 3.10 Linear approximations and differentials
Chapter 4 – Applications of Differentiation
4.1 Maximum and minimum values 4.2 The Mean Value Theorem 4.3 How derivatives affect the shape of a graph 4.4 Indeterminate forms and L’Hospital’s Rule 4.7 Optimization problems 4.8 Newton’s Method 4.9 Antiderivatives
Chapter 5 – Integrals (introduction)
